Non-Categorical Thinking Workshop
EuNoC Workshop #2
The second workshop of the European Non-Categorical Thinking Project will take place at the University of Turin on September 22 and 23, Campus Luigi Einaudi (Lungo Dora Siena 100), room 3D1 36.
22 SEPTEMBER, afternoon session
14.15 | Simon HEWITT (University of Leeds)
Modal plural logic: A plea for humility
ABSTRACT. Modal plural logic is put to important use in contemporary metaphysics, providing the background for one of Williamson's arguments for necessitism and being used to undermine deflationary accounts of the semantics of predication. However, it is nearly universally assumed that correct modal logic of plurals contains strong principles governing the interaction between modals and plurals. We show that formal arguments in support of these, recently explored by Linnebo, fail. It is doubtful that constraints from language usage motivate these principles, and we maintain that therefore a sceptical position ought to be adopted. There may be lessons here for modal logic more generally.
15.30 | Gian Luca POZZATO (Università di Torino)
Internal calculi for Lewis' conditional logics of counterfactual reasoning
ABSTRACT. We provide standard internal sequent calculi for Lewis’ conditional logic V and its extensions VN, VW, VC, VA, VNA. The original motivation by Lewis was to formalize counterfactual sentences, i.e. conditionals of the form “if A were the case then B would be the case”, where A is false. The logic V is the basic logic of counterfactuals in the family of Lewis’ systems. It is characterized by the whole class of so-called sphere models. Our calculi take as primitive Lewis’ connective of comparative plausibility ≼: a formula A ≼ B intuitively means that A is at least as plausible as B. Our calculi are standard in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises. Moreover our calculi are “internal”, in the sense that each sequent can be directly translated into a formula of the language. We show that the calculi provide optimal decision procedures for the respective logics.
16.45 | Katrin SCHULZ (University of Amsterdam)
What Fake Tense can teach us about conditionals
Topic of this talk is the phenomenon of Fake Tense. Fake Tense refers to the observation that in English subjunctive conditionals (though this also holds for many other languages), the Simple Past, and sometimes also the Past Perfect, appear not to be interpreted as semantic past tense or past perfect. Fake tense is directly related to the notoriously problematic distinction between indicative and subjunctive conditionals: you can use fake tense to distinguish between both types of conditionals. In this talk we want to explore in how far understanding fake tense can help us to get a better grasp of the difference between indicative and subjunctive conditionals.
18.00 | Project meeting, led by John DIVERS (University of Leeds)
23 SEPTEMBER, morning session
9.30 | Francesco BERTO (University of Amsterdam)
Intentions for hyperintensions: A new take on logical omniscience
ABSTRACT. I propose a semantic approach to the problem of logical omniscience, taking at face value the understanding of beliefs as intentional states: a subject who believes that p has a mental attitude towards a situation — a configuration of objects and properties — verifying p. The theory is based on (1) a new way to mark the distinction, occurring in the literature of both epistemic logic and cognitive science, between explicit and implicit belief; (2) the modeling of implicit belief as a variably strict quantifier over possible worlds, indexed by explicit belief; (3) the imposition of a content containment requirement for a belief to logically entail another. The semantics invalidates most forms of logical omniscience: cognitive agents can have explicitly inconsistent beliefs without trivially believing everything; logical validities are not generally believed; and belief is not closed under strict implication: an agent can believe p but fail to believe q even when, necessarily, if p then q. However, belief is closed under believed and content-preserving implication.
10.45 | Arif AHMED (University of Cambridge)
Belief, blame, and statistical evidence
ABSTRACT. Recent work in epistemology (e.g. Buchak 2012; Enoch, Specter, et al. 2012) suggests that certain natural responses to statistical data, for instance in the 'Gatecrasher paradox' show that ethical or forensic judgments are subject to norms that are independent of their representational status. I argue that this is an illusion, that the 'natural responses' may lack justification altogether, and that the intuition behind them might be explained by means of social rather than individual norms on the formation of these beliefs that are consistent with their being wholly representational.
12.00 | Hykel HOSNI (Università di Milano)
A logical perspective on prescriptive rationality
We report on ongoing research (in collaboration with Marcello D'Agostino and Tommaso Flaminio) aimed at providing a logic-based, prescriptive theory of rational belief. By this we mean a normative theory which takes into account the cognitive limitations of the agents to be modelled. To this end we build on the theory on Depth-bounded Boolean Logics, which provides a hierarchy of feasible approximations to classical logic.
The event is funded as part of the activities of two ongoing research projects on related issues: Condizionali non materiali (University of Turin) and Exception OWL (Compagnia di Sanpaolo).
For creatures like us, it is natural to think non-categorically — in terms of the possible, the probable, and the conditional. This fact prompts the following philosophical questions. Is non-categorical thinking indispensable, in any sense, to all practical and intellectual life? How should we think of reality and our cognitive relations to it in light of our answers to that question? Is our non-categorical thought an instrument that we need only because of our ignorance of how the world categorically is, or when we think non-categorically do we sometimes track a corresponding (probabilistic, modal or conditional) non-categorical reality? What are the best systematic (formal) representations of non-categorical thinking and how do these relate (normatively or otherwise) to our non-categorical thought? Has the practice of natural science settled some of these questions and if some of the questions are so settled how does that bear on the others? Can we look to the case of mathematics to find models of what practical and intellectual indispensability (of a way of thinking) might amount to and the epistemological and metaphysical implications of these models? The central purpose of the project is to develop questions about modalities, conditionals, and probabilities — in the context of a unified theoretical framework: one that will promote applications of research programmes that have been successful in one sphere of categorical thought to the neighbouring regions.